15

Is there a symbol for the inverse? I have been using X^{-1} for my matrix inversions, but this results in the -1 being rather large and taking up almost as much room as another symbol. Is there a built in symbol or trick I should be using?

7
  • Which symbol are you looking for? – Manuel Jan 12 '15 at 20:38
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    That's the default notation. If you want something different, specify what you want, otherwise this is probably better-suited on Mathematics. – Werner Jan 12 '15 at 20:40
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    @DJP The way you put it, your comment is simply wrong. Matrices are bold in some texts, and are not in another ones. – yo' Jan 12 '15 at 22:11
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    @DJP And you don't understand me. They are not bold in some texts not because the authors of these are idiots, but because they decided that in their context, the bold font for matrices is not appropriate. Likewise, in many contexts vectors do not have arrow, neither they are bold, and it is completely correct. And btw, bold upright font, as you suggest, is wrong, too, according to many. – yo' Jan 12 '15 at 22:23
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    @DJP - On using arrow notation for vectors and/or bold lettering for matrices, see also Is arrow notation for vectors “not mathematically mature”?, posted recently on Math.SE. – Mico Jan 13 '15 at 9:28
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If you just want to reduce the size of the -1 term, you could create your own macro called, say, \inv{...}, along the lines of the code below. The screenshot shows the look of both \inv{X} and X^{-1}. (The vertical offset of 1.15ex is chosen so that the tops of the 1 symbols are at very nearly the same height using either \inv{...} or X^{-1}. Feel free to adjust the offset to suit your preferences.)

enter image description here

\documentclass{article}
\newcommand\inv[1]{#1\raisebox{1.15ex}{$\scriptscriptstyle-\!1$}}
\begin{document}
$X \inv{X} X^{-1}$
\end{document}
4
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    LaTeX has \raisebox – egreg Jan 12 '15 at 20:55
  • @egreg - Thanks. I've changed the code from \raise...\hbox{$...$} to \raisebox{...}{$...$}. – Mico Jan 12 '15 at 21:05
  • As in egreg's answer, I think a superscript would be definitely better. – Manuel Jan 12 '15 at 22:25
  • @Manuel - The posting's title was "Matrix Inverse symbol". :-) As long as the OP uses uppercase Roman letters -- which is admittedly an assumption, though hopefully not a bad one! -- to denote matrices, there's little practical difference between the outputs produced by the two answers. (Only real difference: My code inserts a "negative thinspace" between - and 1 in order to make the expression nice and compact.) Incidentally, I would definitely not recommend using either form of the \inv macro to denote the basic "some generic variable to the power minus one" expression. – Mico Jan 12 '15 at 23:02
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I see nothing bad in the usual notation X^{-1}. Here's a possible redefinition

\documentclass{article}
\usepackage{amsmath}

\newcommand{\inv}{^{\raisebox{.2ex}{$\scriptscriptstyle-1$}}}

\begin{document}
\[
X^{-1}\ne X\inv
\]
\end{document}

enter image description here

4
  • This, seems to me, is quite similar to Mico's answer (may be even a duplicate). In any case, the only relevant difference is that here the \inv command doesn't take an argument: any reasons why is this better? I think \inv{A} is pretty readable and, of course, you definitely have more power if you wan't to change the appearance of how an inverse looks. – Manuel Jan 12 '15 at 22:15
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    @Manuel It's quite different if you look closely, because the superscript will take into account the symbol to which it's appended. Try my macro with \Bigr)\inv and Mico's \inv{\Bigl(...\Bigr)}. Adding an argument changes the natural order. – egreg Jan 12 '15 at 22:21
  • Well, I missed that. Then this is a comment less relevant, I thought Mico included the superscript (I did not look closely enough, I imagined it). Still, if Mico's answer included the ^, you are still dropping here the “feature” of the argument, which gives more power at the end, and there's no problem with readability/understandability. – Manuel Jan 12 '15 at 22:25
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    It is actually rather annoying if you have chains of matrix multiplication involving inverses and transposes such as (A+BX^{-1}D^{T}C) but I don't think we can do anything about it. – percusse Jan 13 '15 at 0:17
1

Maybe this is a completely wrong idea because it is mixing math and text fonts but what about:

\newcommand{\inv}{^{\text{-}1}}

And then you can write stuff like $A - BD\inv C$ in natural order rather than in the prefix order. This gives you a shorter dash so that the inverse does not take up so much space:

inverses

This is using the Euler font. I also tend to define transpose and inverse-transpose (also see What is the best symbol for vector/matrix transpose?):

\newcommand{\tr}{^{\!\top}}
\newcommand{\invtr}{^{\text{-}\!\top}}
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  • I definitely prefer \inv{x} rather than x\inv because (1) it's more readable and (2) you keep the absolute power of the output with \inv{x} and you can change definition with comlete flexibilty. – Manuel Mar 24 '16 at 21:21
  • Thanks for feedback. Well, consider e.g. (A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1}+VA^{-1}U)^{-1}VA^{-1} vs. (A + UCV)\inv = A\inv - A\inv U(C\inv+VA\inv U)\inv VA\inv vs. \inv{(A + UCV)} = \inv{A} - \inv{A}U\inv{(\inv{C}+V\inv{A}U)}V\inv{A}. I find the first two more natural but of course, that's a question of taste. If you don't mind my asking, how is the version with argument more flexible? The one without argument would be able to accommodate all the variants listed here (I think). – the swine Mar 25 '16 at 9:22

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